Consider the following 2 period sequential game. There are two players, Firm 1 and Firm 2. They produce identical goods and these goods are perfect substitutes. The inverse demand function in this market is given by P = 20 (q1 + q2). Firm 1 moves first and choose its output q1. Firm 2 observes Firm 1's decision of q1 and then chooses its output q2.

a) (15 points) Suppose that the cost function of both Firm 1 and 2 is given by Ci(qi) = 4qi. Find all subgame perfect Nash equilibria.

b) (10 points) Now suppose that the cost function of both Firm 1 and 2 is given by Ci(qi) = 4qi + 5 when qi > 0. So both firms face a variable cost of 4 and a fixed cost of 5 if they choose to produce. If a firm chooses to produce nothing (qi = 0) then its total cost is 0. Find all subgame perfect Nash equilibria. Defend all your answers carefully and show every step of your calculations.